Biden is also to attend Congressman Jim Clyburn's World Famous Fish Fry, another event on the circuit for would-be presidential candidates. Biden's son Beau confirmed to the New York Times last month that the vice-president is considering a run, but has not yet made up his mind.

On Thursday Emily's List, the biggest organisation in the US promoting women in politics, launched a national Madam President campaign, to put a woman in the White House. It aims to build a base of voters committed to electing the first US woman president. Although it does not name Clinton, there are no other women candidates, Democratic or Republican, on the horizon for 2016. Emily's List is to hold events in the next few months in Iowa, New Hampshire and Nevada – states that help determine the party presidential nominations.

The airport ceremony in Little Rock attracted mainly state and local officials. The Little Rock municipal airport commission voted last year to rename the airport, in order to recognise three decades of service by the couple to the state and nation. The new name is above the airport entrance.

Clinton, who is working on a book about her time as secretary of state, has several speaking engagements lined up that will attract media attention. She is to speak on US economic recovery at a major Clinton Global Initiative event in Chicago in June which will also be addressed by the New Jersey governor, Chris Christie – a potential Republican presidential nominee.

Pelosi, speaking to a crowd of several hundred in Little Rock, was applauded when she said Clinton was well-qualified for the White House. "Nobody has been first lady and senator and now secretary of state. Putting everything aside that she is a woman, she'd be the best qualified person that we've seen."

Pelosi stressed she had no inside knowledge about whether Clinton planned to run, but added: "Think of the message it sends to women in the world. The most powerful figure in the world is a woman, and she also happens to be the most qualified for the job."

Pelosi reiterated several times that she has "no knowledge of anything except my prayers" with regard to a potential Clinton run.

Analysts think Joe Biden would lose to Hillary Clinton if the two both ran for the 2016 Democratic presidential nomination. Photograph: Brian Snyder/Reuters

He quotes the veteran Democratic presidential strategist Robert Shrum, regarding Clinton: "Because she's a Democrat, I can't say she's the elephant in the room, but she's certainly the dominant donkey. If she decides to run, it'll be almost impossible to prevent her from being the nominee. If she doesn't run, I think Biden's the odds-on favourite."

A Quinnipiac University poll released on Thursday found Clinton with 65% among Democrats and independents against only 13% for Biden and New York governor Andrew Cuomo on 4%. If Clinton was not to run, Biden would jump to 45%, with Cuomo on 15%. Other Democrats who could be in the mix include the Maryland governor, Martin O'Malley, and the Massachusetts governor, Deval Patrick.